# Logarithms

## Log and Exponential Form

Log Form: log(base b)X=Y

Exponential Form: b^y=b

Converting Between Logarithmic and Exponential Form 070-46

## example problems

1. 4^3=64

2.log(base M)Z=T

3. log(base x)32=5 convert and solve for X

1. log(base 4)64=3

2.M^T=Z

3. X^5=32 X=2

## Condensed and Expanded form:

Condensed form: LogAB

Expanded form: LogA+LogB

Condensed form: LogA/B

Expanded form: LogA-LogB

Condensed form: LogA^2

Expanded form: 2LogA

Logarithms : Expanding and Combining , Example 1

1. Logx^2y^4

2. logM^2/K

1. 2logX + 4logY

2. 2logM - logK

## Natural Logs

Natural Base (e) and Natural Logarithms (ln)

## Examples

1. ln3x=2

2. ln(x)+ ln(2x)=2

1. x= 2.4630

2. x=1.9221

## Graphing Logs

To sketch the graph of y = loga x, you can use the fact that the graphs of inverse functions are reflections of each other in the line y = x.

this website has really good notes

Graphing logarithmic functions | Exponential and logarithmic functions | Algebra II | Khan Academy

## example problems

this is a link with problems and then the answers are at the bottom of the page

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